The Stability Of A Class Of Degenerate Neutral Delay Systems

The degenerated neutral delay systems have dual nature of degradation systems and neutral systems, since they consider the effection of time delay, then degenerate neutral systems can fully simulate the problems in actual science profoundly and the research of degradation systems is vital for analysis of theoretical control. In recent years, the analysis stability on degradation systems have attracted most scholars.The judging of stability of degenerate systems is a kind of complex and difficult problem. In this paper, we maily study the stability of degenerated systems with time delay, some obtained results will be improved and perfected. This paper mainly includes the following three parts:1. Focus on the problem of stability of degenerate systems with mixed time delays and uncertainties. By constructing suitable Lyapunov functional and apply the skills of inequality analysis, we obtain some matrix inequality conditions of the stability for the system.2. Study stability problems for a class of degenerate systems with nonlinear uncertainties and Markov switching. Such systems have the switching system and the degenerate characteristics, so we should consider its own particularity when we study these questions. By selecting suitable Lyapunov functional, then combining the techniques of inequality analysis and split matrix, we obtained the sufficient condition of asymptotical stability of degenerate systems.3. Research on the stability problems of uncertain degenerate neutral systems with mixed delays. The uncertainties of system are time-varying and bounded, furthermore we adopt Lyapunov functional, ,when dealing with the derivative of V we don't apply amplification estimates but introduce some appropriate free-weighting matrices. we obtain sufficient conditions of asymptotic stability for the degenerate neutral system by LMI approach. Finally, a simulation example is provided to illustrate the effectiveness of the proposed design approach.